Platonism is the view that there exist abstract (that is, non-spatial, non-temporal) objects. Because abstract objects are wholly non-spatiotemporal, it follows that they are also entirely non-physical (they do not exist in the physical world and are not made of physical stuff) and non-mental (they are not minds or ideas in minds; the are not disembodied souls, or Gods, or anything else along these lines). In addition, they are unchanging and entirely causally inert - that is, they cannot be involved in cause-and-effect relationships with other objects.[1] All of this might be somewhat perplexing; for with all of these statements about what abstract objects are not, it might be unclear what they are. We can clarify things, however, by looking at some examples. Consider the sentence '3 is prime'. This sentence seems to say something about a particular object, namely, the number 3. Just as the sentence 'The moon is round' says something about the moon, so too '3 is prime' seems to say something about the number 3. But what is the number 3? There are a few different views that one might endorse here, but the platonist view is that 3 is an abstract object. On this view, 3 is a real and objective thing that, like the moon, exists independently of us and our thinking (i.e., it is not just an idea in our heads). But according to platonism, 3 is different from the moon in that it is not a physical object; it is wholly non-physical, non-mental, and causally inert, and it does not exist in space or time. One might put this metaphorically by saying that on the platonist view, numbers exist "in platonic heaven". But we should not infer from this that according to platonism, numbers exist in a place; they do not, for the concept of a place is a physical, spatial concept. It is more accurate to say that on the platonist view, numbers exist (independently of us and our thoughts) but do not exist in space and time. Similarly, many philosophers take a platonistic view of properties. Consider, for instance, the property of being red. According to the platonist view of properties, the property of redness exists independently of any red thing. There are red balls and red houses and red shirts, and these all exist in the physical world. But platonists about properties believe that in addition to these things, redness - the property itself - also exists, and according to platonists, this property is an abstract object. Ordinary red objects are said to exemplify or instantiate redness. Plato said that they participate in redness, but this suggests a causal relationship between red objects and redness, and again, contemporary platonists would reject this. Platonists of this sort say the same thing about other properties as well: in addition to all the beautiful things, there is also beauty; and in addition to all the tigers, there is also the property of being a tiger. Indeed, even when there are no instances of a property in reality, platonists will typically maintain that the property itself exists. This isn't to say that platonists are committed to the thesis that there is a property corresponding to every predicate in the English language. The point is simply that in typical cases, there will be a property. For instance, according to this sort of platonism, there exists a property of being a four-hundred-story building, even though there are no such things as four-hundred-story buildings. This property exists outside of space and time along with redness. The only difference is that in our physical world, the one property happens to be instantiated whereas the other does not. Source: http://plato.stanford.edu/entries/platonism/

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